MGMAT Problem

[dewanak]

If a - b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

(1) I only

(2) II only

(3) I and II only

(4) I and III only

(5) II and III only

as per the MGMAT answer is (2)

I am ok with b<0 which comes directly from the equation but i say (3) is the answer.

Lets take the equation:

a-b > a+b
now reverse the equality sign by multiplying with negative

a-b < -a-b
2a <0
which means a< 0

Please suggest if i am doing something wrong

[adiagr]

If a - b > a + b, where a and b are integers, which of the following must be true?

I. a < 0
II. b < 0
III. ab < 0

(1) I only

(2) II only

(3) I and II only

(4) I and III only

(5) II and III only

as per the MGMAT answer is (2)

I am ok with b<0 which comes directly from the equation but i say (3) is the answer.

Lets take the equation:

a-b > a+b
now reverse the equality sign by multiplying with negative

a-b < -a-b
2a <0
which means a< 0

Please suggest if i am doing something wrong

when you are multiplying with negative, it will be

(-a+b) < (-a-b) [you have to multiply left-hand side with (-) also]

b < -b
2b<0

b<0

Aditya

[tim]

Thank you, adiagr..

[Jason.tuyj]

why multiply (-) on each side? why A is not the answer as well?

[Jason.tuyj]

why multiply (-) on each side? why A is not the answer as well?

[jnelson0612]

why multiply (-) on each side? why A is not the answer as well?

Here's how I would work this problem:

a - b > a + b
Subtract a from both sides
-b>b

At this point, I would say wait! When b has a negative sign in front it must be greater than a regular b? b must be a negative number in that case. For example, if b=-4, then -(-4)>-4, because that is 4>-4. We don't know anything about the value of a, so the answer is II only.